Question

the length of a rectangle is 4 m longer than its width. if the perimeter of the rectangle is 60 m, find its length and width. length: m width: m

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ meters. Then the length $l = w + 4$ meters.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 60$ m, we substitute $l$ and $P$ into the formula: $60=2((w + 4)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $60=2(2w + 4)$. Then distribute the 2: $60 = 4w+8$.

Step4: Solve for $w$

Subtract 8 from both sides: $60 - 8=4w$, so $52 = 4w$. Divide both sides by 4: $w=\frac{52}{4}=13$ m.

Step5: Solve for $l$

Since $l = w + 4$, substitute $w = 13$ into the equation: $l=13 + 4=17$ m.

Answer:

length: 17 m
width: 13 m